Answer:
a) The average weight is 199 pounds.
b) The probability that the maximum safe weight will be exceeded is 0.4840 = 48.40%.
c) The probability that the maximum safe weight will be exceeded is 0.3539 = 35.39%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
(a) If 56 people are on the elevator, and their total weight is 11,144 pounds, what is their average weight?
This is 11144 divided by 56, that is 11144/56 = 199 pounds.
Their average weight is 199 pounds.
(b) If a random sample of 56 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
The weights of adult U.S. men have mean 196 pounds and standard deviation 71 pounds, which means that [tex]\mu = 196, \sigma = 71[/tex]
11144 pounds is an average of 199 pounds, so this probability is 1 subtracted by the pvalue of Z when X = 199.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{199 - 196}{71}[/tex]
[tex]Z = 0.04[/tex]
[tex]Z = 0.04[/tex] has a pvalue of 0.5160
1 - 0.5160 = 0.4840
The probability that the maximum safe weight will be exceeded is 0.4840 = 48.40%.
(c) If a random sample of 56 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?
The weights of adult U.S. women have mean 169 pounds and standard deviation 80 pounds, which means that [tex]\mu = 169, \sigma = 80[/tex]
11144 pounds is an average of 199 pounds, so this probability is 1 subtracted by the pvalue of Z when X = 199.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{199 - 169}{80}[/tex]
[tex]Z = 0.375[/tex]
[tex]Z = 0.375[/tex] has a pvalue of 0.6461
1 - 0.6461 = 0.3539
The probability that the maximum safe weight will be exceeded is 0.3539 = 35.39%.
help me i need help pls pls pls
Answer:
B.…….................
translate into algebraic expression four divided by the sum of x and three
[tex]\frac{4}{x+3}[/tex]
sum is addition
I need help
A square and a triangle have equal area. If the triangle has a height of 8 cm and a base of 9 cm, what is the perimeter of the square?
A:
72 cm
B:
6 cm
C:
24 cm
D:
18 cm
Answer:
A 72cm
Step-by-step explanation:
Area of a triangle = 1/2 base x height
= 1/2 × 8× 9 = 36cm2
area of triangle = area of square
36cm2 = 36cm2
area of square = length x breath
= x x x = 36cm3
square has all sides(4) equal
therefore: 36/ 2 = 18cm (one side)
(18 x 18= 36cm3, so area is correct)
hence perimeter = 18+ 18+18+18 = 72cm
The table shows the feeding times of some animals in a zoo. Each feeding session lasts for 20 minutes.
Answer: 12:35 hrs
Step-by-step explanation:
Marlon watches the lions feed in the morning which was at 11:30.
Each feeding session lasts 20 minutes:
= 11:30 + 20
= 11:50 am
Marlon then walks for three quarters of an hour - 45 minutes - before stopping.
= 11:50 + 45
= 12:35 hrs
Is the line through points P(2,-9) and Q(6, -13) perpendicular to the line through points R(5,-1) and
S(1,-5)?
Two lines [tex]y_1,y_2[/tex] are perpendicular if their slopes are in a relation [tex]m_1=-\frac{1}{m_2}[/tex].
So we need to find slopes and if the above relation holds then we can claim the lines are perpendicular.
To find slopes, use slope formula
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
The first slope of a line passing through [tex]PQ[/tex] is
[tex]m_1=\frac{-13-(-9)}{6-2}=\frac{-4}{4}=-1[/tex]
The second slope of a line passing through [tex]RS[/tex] is
[tex]m_2=\frac{-1-(-5)}{5-1}=\frac{4}{4}=1[/tex]
Now check if [tex]m_1=-\frac{1}{m_2}[/tex] is true
[tex]-1=-\frac{1}{1}\implies -1=-1[/tex]
This means the two lines are perpendicular.
Hope this helps.
Evaluate the formula for the perimeter of a parallelogram to solve the problem. Then check all that apply.
First, write the formula for the perimeter of a parallelogram, P = 2l + 2w.
Next, use parentheses when you substitute 8 for l and 6 for w.
After multiplying, add 16 and 12.
Sulio needs 28 feet of fencing.
Sulio needs 48 feet of fencing.
Answer:A-B-C-D
Step-by-step explanation:
Answer:
1234
Step-by-step explanation:
i took the test
A straw is placed inside a rectangular box that is 10 inches by 8 inches by 2 inches, as
shown. If the straw fits exactly into the box diagonally from the bottom left corner to
the top right back corner, how long is the straw? Leave your answer in simplest
radical form.
The length of the straw placed inside a rectangular box with 10 inches by 8 inches by 2 inches is 2√42 inches.
To find the length of the straw, we can use the Pythagorean theorem. The straw acts as the hypotenuse of a right-angled triangle formed by the three dimensions of the box (10 inches, 8 inches, and 2 inches).
Let the length of the straw be represented by 'l'.
According to the Pythagorean theorem:
[tex]l^2 = 10^2 + 8^2 + 2^2[/tex]
[tex]l^2 = 100 + 64 + 4[/tex]
[tex]l^2 = 168[/tex]
Take square root on both sides:
[tex]l = \sqrt{168}[/tex]
[tex]l = \sqrt{4 \times 42}[/tex]
[tex]l = 2 \times \sqrt{42}[/tex]
So, the length of the straw is 2√42 inches in simplest radical form.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ12
Complete question:
A straw is placed inside a rectangular box that is 10 inches by 8 inches by 2 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
When the following inequality is graphed, what will it look like?
2 > f
Answer:
Step-by-step explanation:
A hailstone falls from a cloud at a height of 1,600 ft. If the equation for height as a function of time is h(t) = -16t2 + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the hailstone to hit the ground? [?] seconds
Answer:
10 seconds
Step-by-step explanation:
The function is
[tex]h(t)=-16t^2+\text{Initial height}[/tex]
Initial height = 1600 ft
t = Time taken
[tex]0=-16t^2+1600[/tex]
[tex]\Rightarrow -16t^2=-1600[/tex]
[tex]\Rightarrow t^2=\dfrac{1600}{16}[/tex]
[tex]\Rightarrow t^2=100\\\Rightarrow t=\pm 10[/tex]
So, time taken by the hailstone to reach the ground is [tex]10\ \text{seconds}[/tex].
Answer:
10 seconds
Step-by-step explanation:
5 km
5 km
7 km
Find the surface area
Answer:
190km
Step-by-step explanation:
2(wl + hl + hw)
2 · (5 · 7 + 5 · 7 + 5 · 5) = 190
good luck, i hope this helps :)
(2x³ - 10x² + 4x - 20) / (x - 5) = ?
Step-by-step explanation:
2x³ - 10x² + 4x - 20
= 2x²(x - 5) + 4(x - 5)
= (2x² + 4)(x - 5).
Hence (2x³ - 10x² + 4x - 20) / (x - 5)
= [(2x² + 4)(x - 5)] / (x - 5) = 2x² + 4.
Answer:
2x²+4
Step-by-step explanation:
2x³-10x²+4x-20
2(x³-5x²+2x-10)
x-5
2(x²×(x-5)+2(x-5)
x-5
2(x-5)×(x²+2)
x-5
2(x²+2)
=2ײ+4
If x = 4 units, y = 8 units, and h = 7 units, find the area of the parallelogram shown above using decomposition. A. 28 square units B. 56 square units C. 84 square units D. 112 square units
Answer:
a
Step-by-step explanation:
area of parallelogram is equal to base times height 7 * 4
Find the missing length indicated.ii
How many cubes with side lengths of 1/3 cm does it take to fill the prism
Answer:
Answer:48 cubes
You could fit 48 cubes with side lengths of 1/3 cm inside a rectangular prism with dimensions of 1 cm X 2 2/3 cm X 2/3 cm.
I hope it's helpful!
can someone help plz?.
classify the triangle by its sides, and then by angles
Answer:
riangles can be classified by their sides and by their angles. ... If no sides are the same length, then it is a scalene triangle. If two sides are the same length, then it is an isosceles triangle. If all three sides are the same length, then it is an equilateral triangle.
Step-by-step explanation:
Find dy/dx by implicit differentiation.
cot(y) = 9x – 7y
dy/dx = ?
Answer:
Step-by-step explanation:
owrite down the name of each of these triangles
Answer:
sry I don't know.
if someone answer tell me the answer I also want to know : )
What's the difference between an opened circle on a number line and a closed circle. ( Pls give an example)
Answer:
Open circle: used for < (less than) or > (greater than) because the number is not part of the solution.
Closed circle: used for ≥ (greater than or equal to) or ≤ (less than or equal to) because the number is part of the solution.
Shading:
Shade to the right for > or ≥
Shade to the left for < or ≤
Step-by-step explanation:
2 < x < 5
Place a open circle on 2 with shading to the left and a open circle on 5 with shading to the right.
4 ≤ x ≤ 10
Place a closed circle on 4 with shading to the left and a closed circle on 10 with shading to the right.
Explain why an archaeological matrix is important in archeology
Answer:
The stratigraphic relationships that are documented as a principal part of the record of the excavation form a fundamental part of the overall site record and underpin the relationships between the site's other recorded individual archaeological components.
Step-by-step explanation:
Anyone know the answer
Answer:
S(4) = 2
Step-by-step explanation:
S(n) = n(n - 3) / 2
S(4) = 4(4 - 3) / 2
= 4 x 1 / 2
= 4/2
= 2
Which is an irrational number Square root of 21 3 5/8 2.4141414 or -13
Answer:
i dont know
Step-by-step explanation:
A circle has a diameter with endpoints at (0, 4) and (0, –8). What is the approximate area of the circle?
Answer:
113.04
Step-by-step explanation:
Area of a circle is πr2
π = 3.14
r = 6
πr2 = 113.04
Answer:
[tex]36\pi[/tex]
Step-by-step explanation:
The diameter is:
The Euclidean distance between points (x1, y1) and (x2, y2) is:
sqrt((x1 - x2)^2 + (y1 - y2)^2)
Substitute (x1, y1) = (0, 4) and (x2, y2) = (0, -8):
= sqrt((-0 + 0)^2 + (-(-8) + 4)^2)
= sqrt(12^2)
= 12
or simply:
diameter: 4-(-8)=12
The radius is:
12/2=6 units
The area of the circle:
[tex]\pi r^2=\pi(6^2)=36\pi[/tex]
si hay 3/4 de nieve de chocolate y vainilla el resto y el resto de es de fresa qué fracción total de la nieve es de fresa?
La fraccio total de nieve de fresa es de ¼.
Please show the work.
1. A wheelchair ramp is 4.2 m long. I rises 0.7 . What is its angle of inclination to the nearest degree?
2. A person flying a kite has released 176 m of string and attached the end to the ground. The string makes an angle of 27 degree with the ground. How high is the kite? How far away is the kite horizontally? Answer to the nearest meter.
Answer:
see explanation
Step-by-step explanation:
(1)
The angle of inclination is the angle between the horizontal and the ramp.
Using the sine ratio in the right triangle formed by the ground and the ramp
let x be the angle of inclination, then
sinx = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{0.7}{4.2}[/tex] , then
x = [tex]sin^{-1}[/tex] ([tex]\frac{0.7}{4.2}[/tex] ) ≈ 10° ( to the nearest degree )
(2)
Again there is a right triangle between the ground and the vertical height of the kite, with hypotenuse being length of string.
let y be the height of the kite and x the horizontal distance, then
sin27° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{176}[/tex] ( multiply both sides by 176 )
176 × sin27° = y , then
y ≈ 80m ( to the nearest metre ) ← height of kite
and
cos27° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{176}[/tex] ( multiply both sides by 176 )
176 × cos27° = x , then
x ≈ 157m ( to the nearest metre ) ← horizontal distance
Step-by-step explanation:
[tex]1)
The angle of inclination is the angle between the horizontal and the ramp.
Using the sine ratio in the right triangle formed by the ground and the ramp
let x be the angle of inclination, then
sinx = \frac{opposite}{hypotenuse}hypotenuseopposite = \frac{0.7}{4.2}4.20.7 , then
x = sin^{-1}sin−1 (\frac{0.7}{4.2}4.20.7 ) ≈ 10° ( to the nearest degree )
(2)
Again there is a right triangle between the ground and the vertical height of the kite, with hypotenuse being length of string.
let y be the height of the kite and x the horizontal distance, then
sin27° = \frac{opposite}{hypotenuse}hypotenuseopposite = \frac{y}{176}176y ( multiply both sides by 176 )
176 × sin27° = y , then
y ≈ 80m ( to the nearest metre ) ← height of kite
and
cos27° = \frac{adjacent}{hypotenuse}hypotenuseadjacent = \frac{x}{176}176x ( multiply both sides by 176 )
176 × cos27° = x , then
x ≈ 157m ( to the nearest metre ) ← horizontal distance
[/tex]
)A bag contains 20 marbles of the same size that are blue, green, and red. The probability of picking a blue marble is 20%. The probability of picking a green marble is 50%. Determine the probability of picking a red marble from the bag and then classify the probability of picking a red marble as likely or not likely to occur.
Answer:
If the bag contained 20% of blue marbles and 50% of green marbles than that would mean the bag would contain 30% of red marbles. The probability of picking a red marble from the bag would be considered unlikely.
Step-by-step explanation:
Draw the image of the following segment after a dilation centered at the origin with a scale factor of 2/3
Answer:
Step-by-step explanation:
Let the ends of the given segment are A and B.
Coordinates of A → (8, 6)
Coordinates of B → (12, 12)
If a point (x, y) is dilated by a scale factor 'k' about the origin, rule to be followed,
(x, y) → (kx, ky)
If k = [tex]\frac{2}{3}[/tex]
(x, y) → [tex](\frac{2}{3}x, \frac{2}{3}y)[/tex]
By this rule coordinates of the image points of A and B will be,
A(8, 6) → [tex]A'(\frac{2\times 8}{3},\frac{2\times 6}{3})[/tex]
→ A'(5.3, 4)
B(12, 12) → [tex]B'(\frac{12\times 2}{3}, \frac{12\times 2}{3})[/tex]
→ B'(8, 8)
Now we can get the image of segment AB after dilation by a scale factor of [tex]\frac{2}{3}[/tex].
Tom buys 4 tickets for a concert. The total cost is $85,60. How much does he pay
for each ticket?
Answer:
$21.40 for each ticket
Step-by-step explanation:
Answer:
$21.1
Step-by-step explanation:
Why is the value of x to the nearest tenth?
Answer: 9.4
Step-by-step explanation:
Use intercepts to graph the linear equation –2x + 6y =18
Answer:
First, you solve for y, then you graph the equation.
See picture for how to solve for y (aka put in slope intercept form) and graph.
1/3 is the slope and 3 is the y intercept
Step-by-step explanation:
see photos
